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Measurements of the turbulent flow field through a highly staggered cascade propulsor configuration in the Virginia Tech cascade wind tunnel have been taken. Predictions of the same flow using Rapid Distortion Theory (RDT) were performed. Measurements and predictions were compared. The comparison was oriented to check the aptness of RDT in describing this kind of flow. Since this study represents the initial steps of a major project, the RDT model was kept simple. The non-penetration condition (blade blocking effect) was not modeled and the viscous effects were roughly accounted for. This work reveals the capabilities of RDT in predicting the development of turbulence convected through a highly staggered cascade propulsor configuration formed by non-symmetrical airfoils. This present study was possible thank to the support from the Office of Naval Research, in particular Candace Wark and Pat Purtell, under grant number NAG 00014-99-1-0230. / Master of Science

The physical and mathematical foundations of the Oriented-Eddy Collision turbulence model are provided through a discussion of the Reynolds averaged Navier-Stokes (RANS) equations, probability density functions (PDF), PDF collision models, Reynolds stress transport models (RSTM), and two-point correlations. Behavior of the Oriented-Eddy Collision turbulence model near solid boundaries is examined in depth. The Oriented-Eddy Collision turbulence model treats turbulence in a novel way: the average behavior of a turbulent flow can be modeled as a collection of interacting fluid particles, or eddies, which have inherent orientation. The model is cast in the form of a collection of Reynolds stress transport models. Underlying this approach is a unique PDF collision model that departs from more common PDF methods as it includes orientation information along with the usual position and velocity information. This adds important physics and differentiates it from other PDF collision treatments that return RANS-type models. To operate in physical space, the model is cast as a unique decomposition to the two-point velocity correlation transport equation. The Oriented-Eddy Collision turbulence model accurately captures fast pressure-strain in rapid distortion, which is a major shortcoming of nearly all Reynolds stress transport models. The Oriented-Eddy Collision turbulence model contains no special provisions to satisfy realizability, and maintains frame and coordinate invariance. Models to account for turbulent dissipation, diffusion, and system rotation are presented with canonical benchmark flows for validation. Inhomogeneous, anisotropic cases are also considered. Model to capture non-local pressure effects near solid boundaries are proposed in the form of turbulent eddy reorientation schemes with associated Reynolds stress treatments. These schemes aim to capture the asymptotic approach of the Reynolds stress components and basic turbulent, wall-bounded flows are investigated as a means of validation. Boundary conditions for solid and shear-free surfaces are discussed and several alternatives to the standard viscous diffusion model proposed.

Recently a viscoelastic turbulence closure model, based on that of Townsend (1976), for wind-wave interactions by turbulent wind has been proposed by Sajjadi (2001). In that work, the governing equations of mean and turbulence were linearized and solved analytically using an asymptotic method. In this work the equations derived by Sajjadi were solved numerically for the cases of strong turbulence due to wind over surface of a monochromatic water wave. Vortex shedding has been observed at high wind velocities. Also, a layer of vortices separating the main flow of wind from the water surface was observed from the results for high velocities of wind. A finite difference scheme was devised which is second order accurate. The results were compared with another scheme based on the method of superposition coupled with orthonormalization by Scott andWatts (1977). The two schemes agree reasonably well for high velocities while they differ for low velocities. Two test cases were implemented to test the finite difference scheme. The tests show that the finite difference scheme predicts accurate solutions for inhomogeneous equations, while it fails to capture the accurate solution if a non trivial solution exists for homogeneous equations. This is attributed as the reason for the difference in the results.

This study reports the development and validation of a modified two-equation eddy-viscosity turbulence model for computational fluid dynamics prediction of transitional and turbulent flows. The existing terms of the standard k-w model have been modified to include transitional flow effects, within the framework of Reynolds-averaged, eddy-viscosity turbulence modeling. The new model has been implemented into the commercially available flow solver FLUENT and the Mississippi State University SimCenter developed flow solver U2NCLE. Test cases included flow over a flat plate, a 2-D circular cylinder in a crossflow, a 3-D cylindrical body and three conical geometries, which represent the nose-cones of aerodynamic vehicles such as missiles. The results illustrate the ability of the model to yield reasonable predictions of transitional flow behavior using a simple modeling framework, including an appropriate response to freestream turbulence quantities, boundary-layer separation, and angle of attack.

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